Chapter 11, Problem 88E

Interpretation Introduction

Interpretation:

The diatomic gases are to be identified from the given densities at STP.

Concept Introduction: The Ideal Gas Law is used to calculate the molar mass of the gas.

Using the relation between mass, volume, pressure and number of moles in the Ideal Gas equation, the molar mass of gas is calculated as:

$PV=nRT$

Substitute $n=\frac{m}{\text{Molar}\text{mass}}$ in the above equation as:

$\begin{array}{l}PV=\frac{m}{\text{Molar mass}}RT\\ \text{Molar mass}=\frac{mRT}{PV}\end{array}$

Substitute $\frac{m}{V}=d$ in the above equation to get:

$\text{Molar mass}=\frac{dRT}{P}$

Here, $P$ is pressure, $V$ is volume, $T$ is temperature, $R$ is universal gas constant and $d$ is the density of the gas.

At STP, the volume is $22.4\text{ L}$, the pressure is $1\text{ atm}$ and the temperature is $273\text{ K}$.